{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,2,21]],"date-time":"2025-02-21T11:44:07Z","timestamp":1740138247337,"version":"3.37.3"},"reference-count":51,"publisher":"Informa UK Limited","issue":"6","funder":[{"DOI":"10.13039\/501100004329","name":"Slovenian Research Agency","doi-asserted-by":"publisher","award":["P1-0222 and grants J1-50002, J1-2453, N1-0217, J1-3004"],"award-info":[{"award-number":["P1-0222 and grants J1-50002, J1-2453, N1-0217, J1-3004"]}],"id":[{"id":"10.13039\/501100004329","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":["www.tandfonline.com"],"crossmark-restriction":true},"short-container-title":["Optimization Methods and Software"],"published-print":{"date-parts":[[2024,11]]},"DOI":"10.1080\/10556788.2024.2339221","type":"journal-article","created":{"date-parts":[[2024,7,29]],"date-time":"2024-07-29T13:22:20Z","timestamp":1722259340000},"page":"1263-1308","update-policy":"https:\/\/doi.org\/10.1080\/tandf_crossmark_01","source":"Crossref","is-referenced-by-count":0,"title":["Matrix extreme points and free extreme points of free spectrahedra"],"prefix":"10.1080","volume":"39","author":[{"given":"Aidan","family":"Epperly","sequence":"first","affiliation":[{"name":"Mathematics Department, UC San Diego, La Jolla, CA, USA"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Eric","family":"Evert","sequence":"additional","affiliation":[{"name":"Computer Science Department, Northwestern University, Evanston, IL, USA"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"J. William","family":"Helton","sequence":"additional","affiliation":[{"name":"Mathematics Department, UC San Diego, La Jolla, CA, USA"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Igor","family":"Klep","sequence":"additional","affiliation":[{"name":"Faculty of Mathematics and Physics, University of Ljubljana & Institute of Mathematics, Physics and Mechanics, Ljubljana, Slovenia"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"301","published-online":{"date-parts":[[2024,7,29]]},"reference":[{"key":"e_1_3_4_2_1","doi-asserted-by":"publisher","DOI":"10.4153\/CJM-2014-024-1"},{"key":"e_1_3_4_3_1","unstructured":"J. Agler An abstract approach to model theory in Surveys of Some Recent Results in Operator Theory Vol. II Pitman Research Notes in Mathematics Series Longman Essex 1988 pp. 1\u201323."},{"key":"e_1_3_4_4_1","doi-asserted-by":"publisher","DOI":"10.1007\/BF02392388"},{"key":"e_1_3_4_5_1","doi-asserted-by":"publisher","DOI":"10.1090\/S0894-0347-07-00570-X"},{"key":"e_1_3_4_6_1","doi-asserted-by":"publisher","DOI":"10.1016\/j.jmaa.2020.124457"},{"key":"e_1_3_4_7_1","doi-asserted-by":"publisher","DOI":"10.1007\/s11045-005-6730-7"},{"key":"e_1_3_4_8_1","doi-asserted-by":"publisher","DOI":"10.1137\/1.9781611972290"},{"key":"e_1_3_4_9_1","doi-asserted-by":"publisher","DOI":"10.1007\/s00220-022-04379-w"},{"key":"e_1_3_4_10_1","doi-asserted-by":"publisher","DOI":"10.1063\/1.5049125"},{"key":"e_1_3_4_11_1","volume-title":"Optimization of Polynomials in Noncommuting Variables","author":"Burgdorf S.","year":"2016","unstructured":"S. Burgdorf, I. Klep, and J. Povh, Optimization of Polynomials in Noncommuting Variables, Springer, Berlin, 2016."},{"key":"e_1_3_4_12_1","first-page":"4069","article-title":"Dilations, inclusions of matrix convex sets, and completely positive maps","volume":"13","author":"Davidson K.R.","year":"2017","unstructured":"K.R. Davidson, A. Dor-On, M.O. Shalit, and B. Solel, Dilations, inclusions of matrix convex sets, and completely positive maps, Int. Math. Res. Not. 13 (2017), pp. 4069\u20134130.","journal-title":"Int. Math. Res. Not."},{"key":"e_1_3_4_13_1","doi-asserted-by":"publisher","DOI":"10.1215\/00127094-3165004"},{"key":"e_1_3_4_14_1","doi-asserted-by":"publisher","DOI":"10.1063\/5.0022344"},{"key":"e_1_3_4_15_1","doi-asserted-by":"crossref","unstructured":"M. de Oliveira J.W. Helton S. McCullough and M. Putinar Engineering systems and free semi-algebraic geometry in Emerging Applications of Algebraic Geometry M. Putinar and S. Sullivant eds. New York: Springer-Verlag 2009 pp. 17\u201361.","DOI":"10.1007\/978-0-387-09686-5_2"},{"key":"e_1_3_4_16_1","unstructured":"M. de Oliveira J.W. Helton B. Miller and M. Stankus NCAlgebra 5.04: A noncommutative algebra package for Mathematica Nov. 2017."},{"key":"e_1_3_4_17_1","doi-asserted-by":"crossref","unstructured":"A.C. Doherty Y.-C. Liang B. Toner and S. Wehner The quantum moment problem and bounds on entangled multi-prover games in 23rd Annual IEEE Conference on Computational Complexity IEEE Computer Society Los Alamitos CA 2008 pp. 199\u2013210.","DOI":"10.1109\/CCC.2008.26"},{"key":"e_1_3_4_18_1","first-page":"159","article-title":"Boundary representations for families of representations of operator algebras and spaces","volume":"53","author":"Dritschel M.","year":"2005","unstructured":"M. Dritschel and S. McCullough, Boundary representations for families of representations of operator algebras and spaces, J. Operator Theory 53 (2005), pp. 159\u2013168.","journal-title":"J. Operator Theory"},{"key":"e_1_3_4_19_1","doi-asserted-by":"publisher","DOI":"10.1006\/jfan.1996.2958"},{"key":"e_1_3_4_20_1","doi-asserted-by":"publisher","DOI":"10.7153\/oam-2021-15-85"},{"key":"e_1_3_4_21_1","unstructured":"E. Evert A. Epperly M. de Oliveira J. Yin and J.W. Helton NCSE 2.3: An NCAlgebra package for optimization over free spectrahedra Feb. 2021."},{"key":"e_1_3_4_22_1","doi-asserted-by":"publisher","DOI":"10.1080\/10586458.2021.1980457"},{"key":"e_1_3_4_23_1","doi-asserted-by":"publisher","DOI":"10.1007\/s00208-019-01858-9"},{"key":"e_1_3_4_24_1","doi-asserted-by":"publisher","DOI":"10.1007\/s12220-017-9866-4"},{"key":"e_1_3_4_25_1","doi-asserted-by":"publisher","DOI":"10.1112\/S0024610799008613"},{"key":"e_1_3_4_26_1","doi-asserted-by":"publisher","DOI":"10.1016\/j.laa.2004.06.020"},{"key":"e_1_3_4_27_1","doi-asserted-by":"publisher","DOI":"10.1137\/16M1100642"},{"key":"e_1_3_4_28_1","first-page":"139","article-title":"Boundary representations of operator spaces, and compact rectangular matrix convex sets","volume":"79","author":"Fuller A.H.","year":"2018","unstructured":"A.H. Fuller, M. Hartz, and M. Lupini, Boundary representations of operator spaces, and compact rectangular matrix convex sets, J. Operator Theory 79 (2018), pp. 139\u2013172.","journal-title":"J. Operator Theory"},{"key":"e_1_3_4_29_1","doi-asserted-by":"publisher","DOI":"10.1007\/s10208-018-09410-y"},{"key":"e_1_3_4_30_1","doi-asserted-by":"publisher","DOI":"10.2977\/prims\/1195187876"},{"key":"e_1_3_4_31_1","doi-asserted-by":"publisher","DOI":"10.1007\/s10107-012-0525-z"},{"issue":"1232","key":"e_1_3_4_32_1","first-page":"104","article-title":"Dilations, linear matrix inequalities, the matrix cube problem and beta distributions","volume":"257","author":"Helton J.W.","year":"2019","unstructured":"J.W. Helton, I. Klep, S. McCullough, and M. Schweighofer, Dilations, linear matrix inequalities, the matrix cube problem and beta distributions, Mem. Amer. Math. Soc. 257(1232) (2019), p. 104.","journal-title":"Mem. Amer. Math. Soc."},{"key":"e_1_3_4_33_1","doi-asserted-by":"publisher","DOI":"10.1016\/j.aim.2018.04.007"},{"key":"e_1_3_4_34_1","doi-asserted-by":"publisher","DOI":"10.4007\/annals.2012.176.2.6"},{"key":"e_1_3_4_35_1","doi-asserted-by":"publisher","DOI":"10.1109\/TAC.2009.2017087"},{"key":"e_1_3_4_36_1","doi-asserted-by":"publisher","DOI":"10.1090\/tran\/8418"},{"key":"e_1_3_4_37_1","doi-asserted-by":"crossref","unstructured":"D.S. Kaliuzhnyi-Verbovetskyi and V. Vinnikov Foundations of Free Noncommutative Function Theory volume 199 of Mathematical Surveys and Monographs American Mathematical Society Providence RI 2014.","DOI":"10.1090\/surv\/199"},{"key":"e_1_3_4_38_1","doi-asserted-by":"publisher","DOI":"10.7900\/jot.2011oct22.1927"},{"key":"e_1_3_4_39_1","doi-asserted-by":"publisher","DOI":"10.1007\/s11785-019-00937-8"},{"key":"e_1_3_4_40_1","doi-asserted-by":"crossref","unstructured":"N.H.A. Mai A. Bhardwaj and V. Magron The constant trace property in noncommutative optimization in ISSAC '21\u2014Proceedings of the 2021 International Symposium on Symbolic and Algebraic Computation ACM New York 2021 pp. 297\u2013304.","DOI":"10.1145\/3452143.3465516"},{"key":"e_1_3_4_41_1","doi-asserted-by":"publisher","DOI":"10.1007\/978-1-4939-6942-5"},{"key":"e_1_3_4_42_1","doi-asserted-by":"crossref","unstructured":"P.S. Muhly and B. Solel An algebraic characterization of boundary representations in Nonselfadjoint Operator Algebras Operator Theory and Related Topics Operator Theory Advances and Applications Birkh\u00e4user Basel 1998 pp. 189\u2013196.","DOI":"10.1007\/978-3-0348-8779-3_13"},{"key":"e_1_3_4_43_1","doi-asserted-by":"publisher","DOI":"10.1016\/j.jalgebra.2014.08.053"},{"key":"e_1_3_4_44_1","doi-asserted-by":"publisher","DOI":"10.4171\/dm\/897"},{"key":"e_1_3_4_45_1","doi-asserted-by":"publisher","DOI":"10.1007\/s00023-020-01003-2"},{"key":"e_1_3_4_46_1","doi-asserted-by":"publisher","DOI":"10.1137\/090760155"},{"key":"e_1_3_4_47_1","doi-asserted-by":"publisher","DOI":"10.1016\/j.jfa.2006.07.004"},{"key":"e_1_3_4_48_1","doi-asserted-by":"publisher","DOI":"10.1007\/BF01100204"},{"key":"e_1_3_4_49_1","first-page":"155","article-title":"Free analysis questions II: the Grassmannian completion and the series expansions at the origin","volume":"645","author":"Voiculescu D.-V.","year":"2010","unstructured":"D.-V. Voiculescu, Free analysis questions II: the Grassmannian completion and the series expansions at the origin, J. Reine Angew. Math. 645 (2010), pp. 155\u2013236.","journal-title":"J. Reine Angew. Math."},{"key":"e_1_3_4_50_1","doi-asserted-by":"publisher","DOI":"10.1007\/s10589-021-00301-7"},{"key":"e_1_3_4_51_1","doi-asserted-by":"publisher","DOI":"10.1090\/S0002-9947-99-02364-8"},{"key":"e_1_3_4_52_1","doi-asserted-by":"publisher","DOI":"10.1016\/j.jmaa.2016.07.043"}],"container-title":["Optimization Methods and Software"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.tandfonline.com\/doi\/pdf\/10.1080\/10556788.2024.2339221","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2024,12,23]],"date-time":"2024-12-23T14:47:23Z","timestamp":1734965243000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.tandfonline.com\/doi\/full\/10.1080\/10556788.2024.2339221"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2024,7,29]]},"references-count":51,"journal-issue":{"issue":"6","published-print":{"date-parts":[[2024,11]]}},"alternative-id":["10.1080\/10556788.2024.2339221"],"URL":"https:\/\/doi.org\/10.1080\/10556788.2024.2339221","relation":{},"ISSN":["1055-6788","1029-4937"],"issn-type":[{"type":"print","value":"1055-6788"},{"type":"electronic","value":"1029-4937"}],"subject":[],"published":{"date-parts":[[2024,7,29]]},"assertion":[{"value":"The publishing and review policy for this title is described in its Aims & Scope.","order":1,"name":"peerreview_statement","label":"Peer Review Statement"},{"value":"http:\/\/www.tandfonline.com\/action\/journalInformation?show=aimsScope&journalCode=goms20","URL":"http:\/\/www.tandfonline.com\/action\/journalInformation?show=aimsScope&journalCode=goms20","order":2,"name":"aims_and_scope_url","label":"Aim & Scope"},{"value":"2023-02-20","order":0,"name":"received","label":"Received","group":{"name":"publication_history","label":"Publication History"}},{"value":"2024-03-06","order":2,"name":"accepted","label":"Accepted","group":{"name":"publication_history","label":"Publication History"}},{"value":"2024-07-29","order":3,"name":"published","label":"Published","group":{"name":"publication_history","label":"Publication History"}}]}}